Chemistry Reference
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some.transferability.to.obtain.faster.calculations.although.with.suitable.settings.to.
make.the.PP.harder,.the.TM.PP.can.be.made.almost.perfectly.equivalent.to.the.hard.
Hamann.PP.[54]..Libraries.of.PP.are.often.provided.with.a.solid-state.DFT.code,.but.
those.libraries.are.frequently.incomplete,.or.a.PP.for.an.element.is.found.to.be.inad-
equate..In.those.cases,.the.user.must.construct.his.own.PP,.which.can.be.done.using.
available.code.packages.such.as.fhi98PP.[55].
In. solid-state. calculations,. to. achieve. yet. smoother. orbitals. conducive. to. more.
eficient.calculations,.non-norm-conserving.methods.such.as.the.ultra-soft.potentials.
due.to.Vanderbilt.[56].are.used..Potentials.based.on.the.projector-augmented.wave.
method. [57]. further. extend. this. concept. to. include. some. treatment. of. core. states..
Non-norm-conserving. potentials. are. more. challenging. to. develop. and. add. signii-
cant.complexity.to.code.implementation..Users.of.these.methods.are.often.dependent.
on. atomic. potential. libraries. provided. with. the. code,. and. these. libraries. are. often.
incomplete.or.inadequate.
An.additional.complication.in.many.PPs.used.in.solid-states.physics,.and.almost.
universally. in. plane-wave-based. methods,. is. the. need. to. use. a. separable. approxi-
mation. such. as. the. Kleinman-Bylander. (KB). form. [58],. to. make. the. calculations.
tractable..With.a.spatially.local.PP.and.a.local.basis.set,.the.number.of.matrix.ele-
ments.that.need.to.be.evaluated.scale.linearly.with.the.number.of.atoms..In.contrast.
for.delocalized.plane.waves,.the.computational.cost.of.evaluating.matrix.elements.
over.a.standard.PP.scales.badly.with.the.size.of.the.basis..The.KB.form.recovers.the.
linear.scaling.for.a.plane-wave.basis..However,.the.use.of.KB.often.complicates.the.
construction.of.the.PP,.particularly.avoiding.
ghost states
—artiicial.states.of.the.PP.
that.intrude.into.the.energy.span.of.the.intended.valence.orbitals.and.thereby.corrupt.
a.DFT.calculation..The.PP.generation.codes.have.tools.to.help.identify.the.presence.
of.such.states.in.a.candidate.PP,.but.might.not.provide.an.alternative.that.eliminates.
the.ghost.state.and.leaves.the.candidate.PP.otherwise.intact.
The.art.of.PP.generation.is.not.yet.mature.and.the.creation.of.a.PP.almost.always.
involves. some. compromises.. There. is. no. general. recipe. that. guarantees. success,.
although.some.guidelines.for.how.to.design.and.assess.PP.can.be.found.in.the.lit-
erature.[1]..It.is.possible.to.create.your.own.PPs.if.existing.ones.are.lacking,.but.this.
is.not.a.simple.exercise..The.ultimate.igure.of.merit.is.how.well.a.PP.reproduces.
an.all-electron.calculation,.but.practical.considerations.and.expediency.sometimes.
rule.the.day..This.is.true.even.for.the.authors.of.atomic.PP.libraries.and.it.is.prudent.
to.take.a.skeptical.approach.to.the.use.of.any.PP..The.important.message.is.that.the.
accuracy.of.any.slab-surface.calculation.is.dependent.on.the.quality.of.the.PP.used.in.
the.calculation.and.that.the.quality.of.the.PP.should.never.be.taken.for.granted..We.
will.illustrate.this.principle.below.with.an.example.taken.from.our.own.experience.
6.4.5 c
omPutational
m
odel
for
an
e
rBium
S
urface
To. illustrate. the. full. process. of. generating. a. surface. model. for. a. new. system,. we.
investigate.the.surface.properties.of.erbium.metal,.speciically.the.potential.surface.
reconstructions.and.surface.adsorption/absorption.of.oxygen.and.hydrogen.
The. erbium. system. immediately. dictates. certain. choices. in. the. simulation.
approach..Erbium.is.a.rare.earth.metal,.occurring.late.in.the.lanthanide.series,.the.
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